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AI-GEOSTATS: Linear/Power Models - Responses

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  • Mark Dowdall
    Mark Dowdall email: mark.dowdall@nrpa.no Hello These are selection of the very satisfactory answers I received to my query (detailed below) and posted this
    Message 1 of 1 , Mar 29, 2001
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      Mark Dowdall
      email: mark.dowdall@...





      Hello

      These are selection of the very satisfactory answers I received to my query
      (detailed below) and posted this morning.

      Many thanks to everyone who replied, you've been a big help.

      M.Dowdall

      ****************************************************************************
      Question:

      At the risk of sounding stupid, I need help with something that is probably
      simple. I have a semi-variogram to which I have fitted a linear model. The
      majority
      of texts I read say that the linear model does not have a sill (and, I
      assume a range?). To use this model in GEOEAS,and I quote from the manual,
      "the sill must be chosen so that the corresponding
      'range' parameter value will result in the desired slope". Is this not a
      contadiction ???????
      ****************************************************************************
      Paulo.Ribeiro@...

      In my opinion the problem about the "range" is a terminology one.
      Instead of seen the range parameter as the distance to which the variogram
      "reachs" the sill (or 95% of the sill, for models like the
      exponential) I'd rather think about it as been a simple parameter of the
      correlation (and/or variogram) function.
      Denote the range by $\phi$, and the sill by $\sigma^2$
      for the exponential model the variogram would be
      $$
      \gamma(h) = \sigma^2 ( 1- \exp(- \frac{h}{\phi}) )
      $$
      therefore the function is parametrised by $(\sigma^2, \phi)$ and $\phi$ is
      the value such that $\gamma(\phi) = 0.95 * \sigma^2$


      For the linear model the idea of sill does not makes sense and the
      variogram model would be:
      $$
      \gamma(h) = \beta_0 + \beta_1 h
      $$

      You cannot interpret $(\beta_0, \beta_1)$ the same way you've done with
      $(\sigma^2, \phi)$.
      However, GEOEAS still uses the terminology "sill" and "range".

      Actually, there is a much wider range of options for the variogram
      function than those available in GEOEAS. For each one these things must
      bee understood and checked

      Concluding, I'd rather not to pay too much atttention to the usual idea of
      "range" and "sill". Instead, I thing about them just as parameters of
      variograms functions as for the examples above.
      ***************************************************************************
      benjamin.warr@...

      i think that the book is using one way of 'cheating'. What they are doing is
      using a spherical model to approximate a linear model. You are looking for a
      constant ratio between the sill and the range which gives you a certain
      slope. You then set the range and the sill to values so that to all intents
      and purposes the variogram is linear within the moving neighbourhood,

      ****************************************************************************
      myers@...


      The Truncated Linear Variogram with sill is only valid in 1-dimension and
      hence standard geostatistical software will not include that model. The
      programmers however are "lazy" and instead of providing a separate way to
      put in the parameters for the Linear model (which does not have a sill),
      they use a perhaps confusing scheme. The Linear model is defined by the
      slope so they take the "sill" and the "range" and compute the quotient which
      is then interpreted as the slope. That is, if you want a slope of 2, use a
      range of (for example), 5 and a "sill" of 10. Think of slope as being
      determined by vertical increase divided by horizontal increase.

      *************************************************************************'**
      jeannee@...

      In some sense you're right. The choice of a parameter "slope" would be
      more appropriate, but this would lead GEOEAS to manage different parameters
      compared to other (stationary) models. So, for simplicity, GEOEAS asks you
      to enter a sill and a range (that have no real meaning for the linear model)
      just to calculate the slope of the linear model by the ratio "sill/range".

      ****************************************************************************
      *

      Thanks again
      M.Dowdall

      ****************************************************************************
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